Mixed-Effects shape models for estimating longitudinal changes in anatomy
STIA'12 Proceedings of the Second international conference on Spatio-temporal Image Analysis for Longitudinal and Time-Series Image Data
A hierarchical geodesic model for diffeomorphic longitudinal shape analysis
IPMI'13 Proceedings of the 23rd international conference on Information Processing in Medical Imaging
Geodesic Regression and the Theory of Least Squares on Riemannian Manifolds
International Journal of Computer Vision
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Longitudinal data arises in many applications in which the goal is to understand changes in individual entities over time. In this paper, we present a method for analyzing longitudinal data that take values in a Riemannian manifold. A driving application is to characterize anatomical shape changes and to distinguish between trends in anatomy that are healthy versus those that are due to disease. We present a generative hierarchical model in which each individual is modeled by a geodesic trend, which in turn is considered as a perturbation of the mean geodesic trend for the population. Each geodesic in the model can be uniquely parameterized by a starting point and velocity, i.e., a point in the tangent bundle. Comparison between these parameters is achieved through the Sasaki metric, which provides a natural distance metric on the tangent bundle. We develop a statistical hypothesis test for differences between two groups of longitudinal data by generalizing the Hotelling T2 statistic to manifolds. We demonstrate the ability of these methods to distinguish differences in shape changes in a comparison of longitudinal corpus callosum data in subjects with dementia versus healthily aging controls.